Directional distortional hardening at large plastic deformations

• A theory for directional distortional hardening with large plastic deformations.
• Hardening rules are derived from thermodynamics in terms of corotational rates.
• Corotational rates for fourth order tensors are examined.
• Several choices for plastic spins are considered.
• Results under simple shear loading up to 1000% strain are presented.

This paper extents the directional distortional hardening model of Feigenbaum and Dafalias (2007) into the range of large plastic deformations. This model allows the yield surface to deform such that a region of high curvature develops approximately in the direction of loading and a region of flattening develops on the opposite side. To extend this model into large deformations and in order to ensure positive dissipation and objectivity, hardening rules are derived from thermodynamic conditions in terms of corotational rates. Since this model includes a fourth order tensor-valued hardening internal variable, the corotational rates for fourth order tensors are examined in this work employing the concept of plastic spin. Several choices for plastic spins are presented and used for the simulation of the response under simple shear loading up to 1000% strain.